Assume that automobile accidents at a dangerous intersection occur according to a Poisson process at the rate of 3 accidents per
1 answer:
Answer:
The mean number of serious injuries over a one year's time is of 104 and the standard deviation is of 10.2
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval. The standard deviation is the square root of the mean.
Find the mean and standard deviation of the number of serious injuries over a one year's time.
Per week, mean
A year has approximately 52 weeks, so, the mean is , and the standard deviation is
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Answer:
.
Step-by-step explanation:
Start by separating this decimal number into its integer part and its fraction part:
The most challenging task here is to express as a proper fraction. Once that fraction is found, expressing the original number
will be as simple as rewriting a mixed number as an improper fraction.
Let .
would then represent the original number.
Note that the repeating digits appear in groups of two. Therefore, if the digits in are shifted to the left by two places, the repeating part will continue to match:
.
Note, that this "shifting" is as simple as multiplying the initial number by (same as
raised to the power of the number of digits that needs to be shifted.)
Subtract the original number from the shifted number to eliminate the fraction part completely:
.
In other words:
.
.
Therefore, the original number would be:
.
Recursive equation would be f(x+1) = f(x) - 25 with f(0) = 300
Explicit equation would be f(x) = -25x + 300
And graph would looks like this:
Explicit equation would be f(x) = -25x + 300
And graph would looks like this: